Derivation has been made of the expressions of surface vibrational sum-frequency generation(SVSFG). The results include (a) the vibrational selection rule, (b) the expressions of the susceptibility tensors at the surfaces composed of functional groups with C3v and C2v local symmetry, (c) the formulas of the SFG tensor components which apply specifically to the vibrational resonance with the CH stretching modes of methyl and methylene groups, and (d) the interference effect by the nearby Fermi resonance band. Changes introduced by the slight distortion of C3v symmetry into Cs symmetry have also been discussed. Sample calculations have been made of the SVSFG of the CH stretch modes of oriented CH3 groups.

Comprehensive expressions have been presented to facilitate the analysis of the surface sum-frequency generation (SFG) spectrum. The electric field components of the SFG beam for a given experimental setup have been related via appropriately defined Fresnel coefficients to the nonlinear source polarization, which in turn has been related to the electric fields of exciting visible and infrared beams through the macroscopic SFG susceptibility tensor. The coefficients of transformation have been given to relate the laboratory-fixed Cartesian components of the SFG tensor to the components described in a surface-fixed axis system. The tensor components have been further related to the components of the microscopic hyperpolarizability tensor of surface species, and the explicit expressions (in terms of the Euler angles defining molecular orientation) of the transformation coefficients are presented to describe the Cartesian tensor components described in a surface-fixed axis system by the molecule-fixed components.

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The orientational order of the methyl groups on the surface of cadmium arachidate Langmuir-Blodgett (LB) films with a various number of accumulated monolayers on fused silica has been studied by infrared-visible sum frequency generation (SFG) and Fourier transform infrared absorption (FTIR) spectroscopies. An analysis has been made of the significant in-plane anisotropy of the SFG signals observed for multilayered films and of the change in peak intensities as a function of the number of layers using previously published formulas. The analysis reveals that the SFG signal observed originates from the uppermost layer where the methyl groups are oriented so that the hydrocarbon chains stand perpendicular to the surface with an orthorhombic subcell structure and with the terminal methyl groups inclined away from the direction of withdrawal when the film was prepared. The apparent increase of the SFG signal intensity with number of accumulated layers is ascribed to an increased degree of two-dimensional orientational order of the methyl groups.

Resonance CARS spectrum of perylene in the first excited singlet (S1 ) state was observed in solution at room temperature. The observed shifts of Raman frequencies from the ground (S0 ) state values were related to the results of the PPP-SCF-CI MO calculation and the normal coordinate calculation. The experiment, intended to observe the resonance CARS signal of the S0 state, was found to give the signal predominated by the lines of the S1 state. It was also concluded that the peculiar feature originating from the simultaneous role of the pump beam depleted the molecules in the S0 state, populated the S1 state, and caused the resonance effect on CARS through the intense S1 →S0 transition.